//Given an array of distinct integers nums and a target integer target, return t
//he number of possible combinations that add up to target. 
//
// The test cases are generated so that the answer can fit in a 32-bit integer. 
//
//
// 
// Example 1: 
//
// 
//Input: nums = [1,2,3], target = 4
//Output: 7
//Explanation:
//The possible combination ways are:
//(1, 1, 1, 1)
//(1, 1, 2)
//(1, 2, 1)
//(1, 3)
//(2, 1, 1)
//(2, 2)
//(3, 1)
//Note that different sequences are counted as different combinations.
// 
//
// Example 2: 
//
// 
//Input: nums = [9], target = 3
//Output: 0
// 
//
// 
// Constraints: 
//
// 
// 1 <= nums.length <= 200 
// 1 <= nums[i] <= 1000 
// All the elements of nums are unique. 
// 1 <= target <= 1000 
// 
//
// 
// Follow up: What if negative numbers are allowed in the given array? How does 
//it change the problem? What limitation we need to add to the question to allow n
//egative numbers? 
// Related Topics 数组 动态规划 
// 👍 696 👎 0


package leetcode.editor.cn;

import java.util.ArrayList;
import java.util.Arrays;
import java.util.List;

//Java：Combination Sum IV
public class P377CombinationSumIv {
    public static void main(String[] args) {
        Solution solution = new P377CombinationSumIv().new Solution();
        System.out.println(solution.combinationSum4(new int[]{1, 2, 3}, 32));
        System.out.println(solution.combinationSum42(new int[]{1, 2, 3}, 32));
        // TO TEST
    }

    //leetcode submit region begin(Prohibit modification and deletion)
    class Solution {
        List<List<Integer>> result = new ArrayList();
        int size = 0;

        public int combinationSum4(int[] nums, int target) {
            Arrays.sort(nums);
            combine(nums, target, new ArrayList<>());
            return size;
        }

        public void combine(int[] nums, int target, List<Integer> list) {
            if (target == 0) {
                size++;
                return;
            }
            for (int i = 0; i < nums.length; i++) {
                int num = nums[i];
                if (target - num < 0) {
                    return;
                }
                list.add(num);
                combine(nums, target - num, list);
                list.remove(list.size() - 1);
            }
        }

        public int combinationSum42(int[] nums, int target) {
            int[] dp = new int[target + 1];
            dp[0] = 1;
            for (int i = 1; i <= target; i++) {
                for (int num : nums) {
                    if (num <= i) {
                        dp[i] += dp[i - num];
                    }
                }
            }
            return dp[target];
        }

    }
//leetcode submit region end(Prohibit modification and deletion)

}